P-income, kg/week 9000 8000 7000 6000 Suna 5000 Shuya 4000 Vytegra Vodla 3000 2000 1000 0 0 4 8 12 16 20 24 28 32 36 40 44 48 52 Time, weeks Fig. 8.3. Total P income with main inflow rivers to Lake Onega calculated using LakeWeb load sub- model. The comparison of calculated and measured total phosphorus concentrations shows rather good agreement even in the case of default value of TP concentration 30 mg m-3 used for all rivers (Fig. 8.4). Measured & calculated TP income TP, kg/a 200000 180000 160000 140000 120000 LakeWeb 100000 Measured 80000 60000 40000 20000 0 Suna Shuya Vytegra Vodla Fig. 8.4. Comparison of measured and total phosphorus income calculated using LakeWeb model for the period April 2001-March 2002 (12 months). This simple statistical phosphorus load model was combined with Vollenweider – Canfield – Bachmann lake model (1), (3) into one integrated lake-catchment model. A graphical user interface, GUI (Figs. 8.5 - 8.6) helps to modify input parameters and to visualize the model output. 40 The Finnish Environment 36 | 2009 Fig. 8.5. Input parameters dialog of the integrated lake-catchment model interface. Fig. 8.6. Output window of the lake-catchment model GUI. This model was applied to Petrozavodsk and Kondopoga Bays of Lake Onega. The calculations were organized in the following way. The model was run for several years period with different combinations of mean annual inflow discharge and mean annual inflow concentration of total phosphorus until the periodic solution was achieved. The calculated total phosphorus concentration in lake waters was averaged for the last simulated one year period. These values were tabulated and contour plots of lake TP concentration as a function of mean annual discharge and inflow TP concentration were produced (Figs. 8.7 and 8.8). The Finnish Environment 36 | 2009 41 Total P concentration in inflow, ug/l 100 62 58 80 54 50 46 42 60 38 34 30 40 26 22 18 14 20 10 6 2 20 40 60 80 100 120 140 160 Mean annual discharge, cubic m/s Fig. 8.7. Average annual total phosphorus concentration in Petrozavodsk Bay as a function of inflow discharge and total phosphorus inflow concentration. Total P concentration in inflow, ug/l 120 110 100 44 42 90 40 38 36 80 34 32 30 70 28 26 24 60 22 20 18 50 16 14 12 40 10 8 30 6 4 2 20 10 10 20 30 40 50 60 70 80 90 100 Mean annual discharge, cubic m/s Fig. 8.8. Average annual total phosphorus concentration in Kondopoga Bay as a function of inflow discharge and total phosphorus inflow concentration. 42 The Finnish Environment 36 | 2009 These diagrams can be used for quick estimates of TP concentration in Petroza- vodsk and Kondopoga Bays under different hydrological conditions. The whole pro- cedure can be described as follow: using non-exceedence probability curves of River Shuya (Fig. 8.9, Petrozavodsk Bay tributary) and River Suna (Fig. 8.10, Kondopoga Bay tributary) the mean annual discharge values of specific non-exceedence probabi- lity can be obtained. Using this value and the inflow total phosphorus concentration the resulting lake TP concentration can be easily estimated from diagrams (Figs.8.7 and 8.8). Of course, the limitations of the box models should always be kept in mind when using these diagrams, but, nevertheless, it appears that this method is a useful simple approach to estimate the effects of possible changes in the system catchment- lake on in-lake TP concentration. Non-exceedence probability curve - Shuya - V. Besovets Mean annual discharge, cubic m/s 250 200 150 100 50 0 0.01 0.1 1 10 100 Probability of non-exceedence, % Fig. 8.9. Non-exceedence probability curve – River Shuya – V. Besovets site. Non-exceedence probability curve - Suna -Porosozero Mean annual discharge, cubic m/s 80 70 60 50 40 30 20 10 0 0.01 0.1 1 10 100 Probability of non-exceedence, % Fig. 8.10. Non-exceedence probability curve – River Suna – Porosozero site. The Finnish Environment 36 | 2009 43 8.2 Application of Danish phosphorus model P2 to Kondopoga Bay As it was described earlier the Kondopoga Bay is a receiver of wastewaters from Kondopoga PPM for more than 70 years. Every year nearly 3000 tons of suspended matter, 8 tons of oil products, 4 tons of methanol, 60 tons of P, 80 tons of N, 147 tons of chlorides, 9 tons of formaldehyde, 2000 tons of lignosulphonates are withdrawn to the bay (Belkina 2005). The Danish model for P retention in lakes has two state variables (HELCOM 2006): Pl – total phosphorus concentration in lake water and Ps – exchangeable total P in sediments. Driving parameters in the model are: Pi – inflow total P concentration, Q – water discharge and T – lake water temperature. dP Q l = (k ⋅ P − P )− S + R, dt V i l dP Q s = ((1− k)⋅ P )+ S − R, dt V i 1 k = , V 1+ (5) 365⋅Q P S = a ⋅(1+ C )T −20 ⋅ l , 1 H T −20 R = b⋅(1+ C2 ) ⋅ Ps Here V is the lake volume, m3, Q – inflow discharge, 3m day-1, H – lake depth, m, S – sedimentation, R – release of TP from sediments to lake water, a – sedimentation -2 -1 rate of TP, g P m day , C1 – temperature correction for a, b – release rate of TP, g P -2 -1 m day , C2 – temperature correction for b, T is the water temperature. Calibrated values of parameters on the basis of data from 16 lakes (HELCOM 2006) are: sedimentation rate a=0.047, temperature dependence of P-sedimentation C1 = 0.0, sediment release rate b=0.000595, temperature dependence of P- release C2 = 0.08. 44 The Finnish Environment 36 | 2009 T-20 By introducing new parameters: A=Q/V+a/h, B=b(1+C2) , C=Q/V*k*Pi, E= C=Q/V*(1-k)*Pi, the system of equations can be rewritten in matrix-vector form: Qk V P′ = M ⋅ P + • Pi , Q(1− k) V Pl P = , (6) Ps − A B M = Q . A − − B V Characteristic equation is the following: (7) The eigenvalues are : (8) It should be noted that both eigenvalues are negative for all combinations of parame- ters. For systems of order ≤ 2 this is necessary and sufficient condition of stability. The stationary solution of the system can be obtained in the closed form: P = P , l i Q a (9) ⋅(1− k) + = V H ⋅ Ps T −20 Pi b⋅(1+ C2 ) For example, in Kondopoga Bay mean annual discharge (River Suna) QSuna equals 44.3 m3 s-1, the income of TP with river water is 28 tons a-1 , then mean total phosphorus -3 3 -1 concentration is PSuna=0.0115 g m . Kondopoga PPM produced 0.0529 km a of sewa- ge waters in 1992-1996 (Filatov et al. 1999), the income of TP with sewage water was -1 -3 66.5 tons a , which gives PPPM=1.2571 g m , Pi=(QSunaPSuna+QPPMPPPM)/(QSuna+QPPM)= 0.0381 g m-3. Then using the steady-state solution (10) we will get for lake waters -3 -3 Pl=0.0381 g m , and for bottom sediments Ps=0.383 g m at Twater=10 ºC. The Finnish Environment 36 | 2009 45 Calculated TP concentration in lake water P concentration [ug/l] 35 30 25 20 Presentload 15 without PPM load 10 5 0 1.1. 1.3. 30.4. 29.6. 28.8. 27.10. 26.12. 24.2. 25.4. 24.6. 23.8. 22.10. 21.12. 2000 2001 Time Fig. 8.11. Calculated variation of phosphorus concentration in Kondopoga Bay waters during peri- od 2000 – 2001 with present and without Kondopoga PPM loading. Calculated TP concentration in bottom sediments P concentration [ug/l] 400 350 300 Presentload 250 withoutPPM load 200 150 100 1.1. 1.3. 30.4. 29.6. 28.8. 27.10. 26.12. 24.2. 25.4. 24.6. 23.8. 22.10. 21.12. 2000 2001 Time Fig. 8.12. Calculated variation of phosphorus concentration in bottom sediments during period 2000 – 2001 with present and without Kondopoga PPM loading. Figures 8.11 and 8.12 show examples of phosphorus concentration changes with time during two years period in lake water and bottom sediments calculated with P2 mo- del. Two cases were considered: with present loading from Kondopoga PPM (66.5 tons a-1) and without industrial loading. In the latter case the inflow concentration -3 Pi=0.011 g m . 46 The Finnish Environment 36 | 2009 8.3 Aquatox model – box-type model for aquatic ecosystems Short description of the model AQUATOX (Park & Clough 2004) predicts the fate of various pollutants, such as nutrients and organic chemicals, and their effects on the ecosystem, including fish, invertebrates, and aquatic plants. AQUATOX simulates the transfer of biomass, energy and chemicals from one compartment of the ecosystem to another. It does this by simultaneously computing each of the most important chemical or biological processes for each day of the si- mulation period; it is a process-based or mechanistic model. AQUATOX can predict not only the environmental fate of chemicals in aquatic ecosystems, but also their direct and indirect effects on the resident organisms. Therefore it has the potential to establish causal links between chemical water quality and biological response and aquatic life uses. AQUATOX is the only general ecological risk model that represents the combin- ed environmental fate and effects of conventional pollutants, such as nutrients and sediments, and toxic chemicals in aquatic ecosystems.